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Write a^4 - 3a^2 + 9 - 7 as a product of two monic quadratics with integer coefficients.

 May 22, 2022
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We let \(b = a^2\).

 

We can simplfy the equation to: \(b^2 -3b+2\)

 

To factor, we need a pair of numbers that multiply to 2 and add to -3. 

 

We see that the only pair satisfying this is -2 and -1. 

 

Now, we can rewrite as: \(b^2 - b + 2b + 2\)

 

Factoring the first 2 terms and the last 2 terms seperately gives us: \(b(b-1) - 2(b-1)\)

 

We can add these to get: \((b-2)(b-1)\).

 

Can you take it from here?

 May 22, 2022

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